GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 03:13

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

what is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ?

Author Message
TAGS:

Hide Tags

VP
Joined: 31 Oct 2013
Posts: 1467
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
what is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ?  [#permalink]

Show Tags

Updated on: 05 Mar 2019, 21:26
2
00:00

Difficulty:

(N/A)

Question Stats:

51% (02:11) correct 49% (02:01) wrong based on 90 sessions

HideShow timer Statistics

What is the value of $$0.1 + 0.1^{\frac{1}{m}} + 0.1^{\frac{1}{n}}$$?

(1) $$\frac{1}{m}+ \frac{1}{n} = \frac{4}{3}$$

(2) mn = 3.

Originally posted by KSBGC on 05 Mar 2019, 16:08.
Last edited by Bunuel on 05 Mar 2019, 21:26, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 8003
Re: what is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ?  [#permalink]

Show Tags

05 Mar 2019, 19:54
1
selim wrote:
What is the value of $$0.1 + 0.1^{1/m} + 0.1^{1/n}$$?

1) $$1/m + 1/n = 4/3$$

2) mn = 3.

$$0.1 + 0.1^{\frac{1}{m}} + 0.1^{\frac{1}{n}}=\frac{1}{10} + \frac{1}{10}^{\frac{1}{m}} + \frac{1}{10}^{\frac{1}{n}}=\frac{10^{m+n}+10^{m+1}+10^{n+1}}{10^{m+n+1}}$$
So, we require values of m and n..

When we combine statement 1 and statement 2, we get m and n as 1 and 3 in any order. When we substitute (m =3 and n=1) or (m=1 and n=3), we will get the same answer.
$$\frac{10^{m+n}+10^{m+1}+10^{n+1}}{10^{m+n+1}}=\frac{10^{1+3}+10^{1+1}+10^{3+1}}{10^{1+3+1}}=\frac{10^4+10^2+10^4}{10^5}=\frac{20100}{100000}=\frac{201}{1000}$$=0.201

C
_________________
Manager
Joined: 11 Dec 2018
Posts: 61
Re: what is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ?  [#permalink]

Show Tags

06 Mar 2019, 07:03
Can someone please explain this in detail!?

Posted from my mobile device
Manager
Joined: 16 Oct 2011
Posts: 107
GMAT 1: 570 Q39 V41
GMAT 2: 640 Q38 V31
GMAT 3: 650 Q42 V38
GMAT 4: 650 Q44 V36
GMAT 5: 570 Q31 V38
GPA: 3.75
Re: what is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ?  [#permalink]

Show Tags

06 Mar 2019, 07:18
1
Poorvi55 wrote:
Can someone please explain this in detail!?

Posted from my mobile device

What is the value of .1 +.1^1/m +.1^1/n

We need to know the values of m and n to evaluate the above expression

(1) 1/m +1/n = 4/3. We can several combinations of values for m and n that will give us different values for our expression

let 1/m = 1/3 and let 1/n =1, then our expression becomes .1+.1^1/3 + .1 = .2 +.1^1/3

Let 1/m =2/3 and let 1/n =2/3, then our expression becomes .1 +.1^2/3 +.1^2/3

Since we get two different values for our expression we can mark NS

(2) mn = 3

Let m =1 and n =3. Then our expression becomes .1 + .1^1 + .1^3 = .1+.1 + .001 = .201

Let m = 3/2 and n =2. Then our expression becomes .1 + .1^3/2 + .1^2 = .11 + .1^3/2

Since we get two different values for our expression we can mark NS

(1) and (2). This gives us two equations that we can use to solve for m and n. From (2) m =3/n. We can substitute into (1) to get 1/(3/n) + 1/n =4/3.

This is 1 variable in 1 equation, so we can solve for n, which allows us to solve for m. Sufficient.
Intern
Joined: 24 Feb 2019
Posts: 5
Location: Brazil
Concentration: Strategy, General Management
GPA: 2.96
Re: what is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ?  [#permalink]

Show Tags

11 Mar 2019, 12:50
KSBGC wrote:
What is the value of $$0.1 + 0.1^{\frac{1}{m}} + 0.1^{\frac{1}{n}}$$?

(1) $$\frac{1}{m}+ \frac{1}{n} = \frac{4}{3}$$

(2) mn = 3.

Since we have m and n as exponents in two separated terms from the equation, and those terms are being added together (so we cannot "merge" them like if they were being multiplied), we will need to figure out a way to find both $$m$$ as well as $$n$$.

(1) gives us one equation with 2 variables. This is not enough to solve for both of them, and thus is insufficient.

(2) gives us, again, one equation with 2 variables. Insufficient.

(1) + (2) gives us two equations for two variables, which can be solved. $$\frac{1}{m}+ \frac{1}{n} = \frac{m + n}{mn} = \frac{4}{3}$$.
From this, $$m+n = 4$$, and $$m = (4 - n)$$.

$$m * n = 3$$

$$(4 - n) * n = 3$$

$$n^2 - 4n + 3 = 0$$

$$n = 3$$ or $$n = 1$$.

If n = 3, m = 1. On the other hand, if n = 1, m = 3.

Now, since the terms to the power of $$\frac{1}{m}$$ and $$\frac{1}{n}$$ are both at the same base ($$0.1$$), it doesn't matter whether $$(m,n) = (1,3)$$ or $$(m,n) = (3,1)$$. Both will give the same final result, and this means that (1) and (2) together are sufficient.

Intern
Joined: 12 Feb 2019
Posts: 17
Re: what is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ?  [#permalink]

Show Tags

11 Jun 2019, 08:31
If we Consider statement 1,
adding both the terms gives us the equation M+N/MN=4/3

Doesn't it tells us that M+N=4
&
MN=3
Re: what is the value of 0.1 + 0.1^(1/m) + 0.1^(1/n) ?   [#permalink] 11 Jun 2019, 08:31
Display posts from previous: Sort by